Chapter 11.1, Problem 37E

To determine

To discuss: The validity of the statement “If f is a continuous function on $\left[1,\infty \right)$ such that $f\left(x\right)>0$ for all x and $f\left(x\right)\ge 10$ for $1\le x\le 1,000$, then ${\displaystyle {\int }_1^{\infty }f\left(x\right)dx}$ diverges”.